Differentiation/Integration basics Flashcards
1
Q
d/dx (a) (or any other constant) = ?
A
0, the derviative of a constant is zero
2
Q
d/dx (x) = ?
A
1
3
Q
d/dx (x^2) = ?
A
2x
4
Q
d/dx (3x^2) = ?
A
6x
5
Q
What is the general rule of differentiation?
A
d/dx (x^n) = nx^(n-1)
6
Q
What is the general rule of differentiation?
when the variable has a coefficient
A
d/dx (ax^n) = nax^(n-1)
7
Q
what is this symbol: ∫
A
Integral symbol
8
Q
∫(x)dx = ?
A
(x^2)/2
9
Q
∫(x^2)dx = ?
A
(x^3)/ 3
10
Q
∫(4x^3)dx = ?
A
x^4
11
Q
What is the general rule of differentiation?
A
∫(x^n)dx = (x^(n+1))/(n+1)
12
Q
What is the general rule of differentiation?
when the variable has a coefficient
A
∫(ax^n)dx = (ax^(n+1))/(n+1)
13
Q
∫(a)dx = ?
or any other constant
A
(ax^(0+1))/(0+1)
= ax
14
Q
When is the derivative equal to the gradient?
A
When the limit of Δx tends to zero
